Super-resolution processing is an image-processing technique for restoring or creating a high-resolution, high-quality image from a low-resolution, low-quality image that has been degraded due to observation or other reasons or taken with a low-resolution imaging device. With the development of high-definition television sets (and similar receivers) and various types of high-definition display devices in recent years, the super-resolution processing has been one of the most important techniques in the field of image processing.
Examples of commonly known super-resolution processing methods include the bilinear method, bicubic method and Lanczos method. Any of these methods is a type of data interpolation method using a linear filter having a low-pass characteristic. Such a method has the advantage that it can be easily implemented in practical systems since the processing can be performed with a relatively small amount of computation and a small amount of processing load on hardware components. However, this method is unsuitable for the reproduction of high-frequency components and therefore hardly applicable to the restoration or creation of an image without losing the sharpness on the edges of the image.
In recent years, a super-resolution processing method using total variation (TV) regularization has been proposed (for example, refer to Non-Patent Document 1). In this technique, the total fluctuation of a restored image is minimized by using statistical information of the noise. An advantage of this technique exists in that image degradation due to ringing or overshooting can be prevented while maintaining the sharpness on the edges of the image. However, this technique is unsuitable for real-time processing, because, in principle, it requires iterative computation to solve an optimization problem, which inevitably involves an enormous amount of computation. Furthermore, due to the high processing load on the hardware components, this technique is difficult to be implemented in a low-cost system.
Over the years, and particularly in the field of digital audio technology, the present inventors have continued research in the attempt of introducing sampled-data control theory (more specifically, sampled-data H∞ (H-infinity) control), which enables the handling of continuous-time characteristics, into digital-to-analogue conversion, sampling-rate conversion and similar techniques for handling digital audio signals (refer to Patent Documents 1 and 2). The technique was aimed at enhancing sound quality to the highest or nearly highest level in terms of audibility as analogue audio by designing a digital filter for digital-to-analogue conversion or sampling-rate conversion which not merely handled the sampled original digital signals as discrete-time signals but also took into account the analogue characteristics contained in the intersample behavior.
Furthermore, in view of the recent development in image compression techniques and the necessity for a corresponding improvement of image quality, the present inventors have been conducting intensive research in the attempt of applying the basic idea of the aforementioned audio signal processing, i.e. sampled-data H∞ optimization, to image processing techniques, such as noise removal or resolution conversion. One example is the image noise removal method proposed in Patent Document 3, by which a high level of image quality, which maintains good properties of the original image, can be achieved while suppressing the block noise or mosquito noise, which are likely to appear in MPEG videos or other compressed images when the compression ratio is high. Non-Patent Documents 2 and 3 disclose a resolution convertor capable of converting the resolution of an image by a desired factor by performing intersample interpolation using a digital filter designed on the basis of sampled-data H∞ optimization.